breathing LED

hello, this is a project i am working on currently

#include <Adafruit_NeoPixel.h>
#include <math.h> 

#define BUTTON_PIN   2    // Digital IO pin connected to the button.  This will be
                          // driven with a pull-up resistor so the switch should
                          // pull the pin to ground momentarily.  On a high -> low
                          // transition the button press logic will execute.

#define PIXEL_PIN    6    // Digital IO pin connected to the NeoPixels.

#define PIXEL_COUNT 12

// Parameter 1 = number of pixels in strip,  neopixel stick has 8
// Parameter 2 = pin number (most are valid)
// Parameter 3 = pixel type flags, add together as needed:
//   NEO_RGB     Pixels are wired for RGB bitstream
//   NEO_GRB     Pixels are wired for GRB bitstream, correct for neopixel stick
//   NEO_KHZ400  400 KHz bitstream (e.g. FLORA pixels)
//   NEO_KHZ800  800 KHz bitstream (e.g. High Density LED strip), correct for neopixel stick
Adafruit_NeoPixel strip = Adafruit_NeoPixel(PIXEL_COUNT, PIXEL_PIN, NEO_GRB + NEO_KHZ800);

bool oldState = HIGH;
int showType = 3;

void setup() {
  pinMode(BUTTON_PIN, INPUT_PULLUP);
  pinMode(11, OUTPUT);
  strip.begin();
  strip.show(); // Initialize all pixels to 'off'
}

void loop() {
  // Get current button state.
  bool newState = digitalRead(BUTTON_PIN);

  // Check if state changed from high to low (button press).
  if (newState == LOW && oldState == HIGH) {
    // Short delay to debounce button.
    delay(20);
    // Check if button is still low after debounce.
    newState = digitalRead(BUTTON_PIN);
    if (newState == LOW) {
      showType++;
      if (showType > 2)
        showType=0;
      startShow(showType);
    }
  }

  // Set the last button state to the old state.
  oldState = newState;
}

void startShow(int i) {
  switch(i){
    case 0: colorWipe2(strip.Color(0, 0, 0), 0);    // Black/off
            break;
    case 1: colorWipe(strip.Color(0, 0, 25), 0);  // Orange
            break;
    case 2: colorWipe(strip.Color(40, 15, 0), 0);  //Blue
            break;
  }
}

// Fill the dots one after the other with a color
void colorWipe(uint32_t c, uint8_t wait) {
  for(uint16_t i=0; i<strip.numPixels(); i++) {
    strip.setPixelColor(i, c);
    strip.show();
    delay(35);
  }
}
// Fill the dots one after the other with a color
void colorWipe2(uint32_t c, uint8_t wait) {
  for(uint16_t i=0; i<strip.numPixels(); i++) {
    strip.setPixelColor(i, c);
    strip.show();
    delay(35);
  }
}

and i want to add an LED on pin 11 to breathe, like a mac on standby, when its showing case 0.

i found this code that i like

#include <math.h>

void setup()
{
  pinMode(11, OUTPUT);
}

void loop()
{
  float val = (exp(sin(millis()/2000.0*PI)) - 0.36787944)*108.0;
  analogWrite(11, val);
}

i started adding in the setup and the library but im not sure if i did those right or how to make the led breathe on case 0?

i started adding in the setup and the library but im not sure if i did those right

You want us to guess? OK. I'll guess that you didn't.

or how to make the led breathe on case 0?

Add an if statement, and the code to write to the pin to loop().